Question: Simplify; express your answer in exponential form. Assume $q\neq 0, n\neq 0$. $\dfrac{{q^{-4}n^{-3}}}{{(q^{4}n^{-1})^{-5}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${q^{-4}n^{-3} = q^{-4}n^{-3}}$ On the left, we have ${q^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${q^{-4} = q^{-4}}$ Apply the ideas above to simplify the equation. $\dfrac{{q^{-4}n^{-3}}}{{(q^{4}n^{-1})^{-5}}} = \dfrac{{q^{-4}n^{-3}}}{{q^{-20}n^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-4}n^{-3}}}{{q^{-20}n^{5}}} = \dfrac{{q^{-4}}}{{q^{-20}}} \cdot \dfrac{{n^{-3}}}{{n^{5}}} = q^{{-4} - {(-20)}} \cdot n^{{-3} - {5}} = q^{16}n^{-8}$